A Descriptive Framework for the Multidimensional Medical Data Mining and Representation

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1 Journal of Computer Siene 7 (4): , 011 ISSN Siene Publiations A Desriptive Framework for the Multidimensional Medial Data Mining and Representation Veeramalai Sankaradass and Kannan Arputharaj Department of Information Siene and Tehnology, College of Engineering, Anna University, Chennai-5, Tamil Nadu, India Abstrat: Problem statement: Assoiation rule mining with fuzzy logi was explored by researh for effetive datamining and lassifiation. Approah: It was used to find all the rules existing in the transational database that satisfy some minimum support and minimum onfidene onstraints. Results: In this study, we propose new rule mining tehnique using fuzzy logi for mining medial data in order to understand and better serve the needs of Multidimensional Breast aner Data appliations. Conlusion: The main objetive of multidimensional Medial data mining is to provide the end user with more useful and interesting patterns. Therefore, the main ontribution of this study is the proposed and implementation of fuzzy temporal assoiation rule mining algorithm to lassify and detet breast aner from the dataset. Key words: Data disretization, fuzzy logi, Assoiation Rule Mining (ARM), Minimum Desription Length (MDL), medial data mining, multidimensional data INTRODUCTION A temporal Assoiation rule is a well established data mining tehnique used to disover o-ourrenes of items mainly in temporal sequene data where the data items in the database are usually reorded as binary data (present or not present). Many tehniques are available in the literature aims to find assoiation rules (with strong support and high onfidene) in large datasets. For example, Classial Assoiation Rule Mining (ARM) (Mahafzah et al., 009) deals with the relationships among the data items present in Multidimensional databases. Similarly, there are a few works that fous on temporal data mining. Temporal rule mining is onerned with data mining of large sequential data sets. Sequential data (Vijayalakshmi and Mohan, 010), mining deals with the mining of data that is ordered with respet to some index. The sope of temporal data mining (Alalá-Fdez et al., 009) extends beyond the standard foreast or ontrol appliations of time series analysis. Often temporal data mining methods must be apable of analyzing data sets that are prohibitively large for onventional time series modeling tehniques to handle effiiently. Problem statement: Due to tremendous advanes and ahievement in biomedial, bioinformatis, biologial and linial data is being mined at tremendous speed. Thus the biologial sequene data (Hu et al., 009) stored at data warehouse in the format of ultidimensional temporal sequential data an be used for finding temporal pattern (Intan and Yenty, 008). Moreover, due to the highly distributed unontrolled mining and use of a wide variety of bio medial data, data olletion, data analysis and semanti integration of suh heterogeneous and widely distributed temporal sequene data has beome an important task for systemati and oordinated analysis of medial dataset (Khan et al., 010). Bio medial data analysis and integration beomes very diffiult due to data omplexity, distribution, volume of data. Most ommerial data mining produts provide large number of modules and tools for performing various data mining tasks but few provide intelligent assistane for addressing many important deisions that must be onsidered during the mining proess. Multi objetive assoiation rule mining with minimum support and minimum onfidene is suitable for datamining analysis (Hamid Reza Qodmanan, et al., 011). Traditional data analysis tehniques annot support huge and omplex medial data set. New data analysis tehnique suh as data mining an be helpful in analysis large and omplex medial sequene data set. Researhers may need data and knowledge whih was disovered by other researhers for their researh that is distributes multidimensional sequential data format. New Corresponding Author: Veeramalai Sankaradass, Department of Information Siene and Tehnology, College of Engineering, Anna University, Chennai-5, Tamil Nadu, India 519

2 systems are needed to manage, Integrate and analyze large &omplex medial data from data warehouses. Not only the evaluation estimation and analysis of data is important but providing the intelligent assistane in equally important. Mostly analysis produts do not provide the intelligent assistant in deision making proess (Papageorgiou, 011). Fuzzy assoiation rule will be suitable for multidimensional data analysis (Hong et al., 009; Weng and Chen, 010; Wu et al., 010). In this study, we propose a fuzzy temporal (Ch. S. Reddy and KVSVN Raju, 009) assoiation rule mining algorithm for effetive temporal datamining. These rules are further used for the lassifiation of breast aner data and it has been found that aurate predition of breast aner is possible with the proposed fuzzy temporal assoiation rule mining algorithm. A Bayesian network onsists of a strutural model and a set of onditional probabilities. The strutural model is a direted graph in whih nodes represent attributes and ars represent attribute dependenies. Attribute dependenies are quantified by onditional probabilities for eah node of given its parents. Bayesian networks (Khan et al., 010) are often used for lassifiation problems, in whih a learner attempts to onstrut a lassifier from a given set of training examples with lass labels. Assume that A1;A;...An are n attributes (orresponding to attribute nodes in a Bayesian network). An example E is represented by a vetor <a1; a;... ; an>, where ai is the value of Ai. Let C represent the lass variable (orresponding to the lass node in a Bayesian network). We use to represent the value that C takes and to denote the lass of E. The lassifier represented by a general Bayesian network is defined in (1): J. Computer Si., 7 (4): , 011 (E) = arg max P()P(a,a,...,a ) C 1 n Assume that all attributes are independent given the lass (onditional independene assumption), the resulting lassifier is alled naive Bayes (Khan et al., 010): (E) = arg max P() P(ai ) C n i= l In naive Bayes, eah attribute node has the lass node as its parent, but does not have any parent from attribute nodes. Beause the values of p and P an be easily estimated from training examples, naive Bayes is easy to onstrut. Naive Bayes is the simplest form of Bayesian networks (Khan et al., 010). It is obvious that Fig. 1: Arhiteture of intelligent data modeling. the onditional independene assumption in naive Bayes is rarely true in reality, whih would harm its performane in the appliations with omplex attribute dependenies. Based on the theory of Bayesian networks, Naive Bayes is a simple yet onsistently performing probabilisti model. Data lassifiation with naive Bayes (Khan et al., 010) is the task of prediting the lass of an instane from a set of attributes desribing that instane and assumes that all the attributes are onditionally independent given the lass. Prediting the lass of an instane are done through utility independent privay preserving data mining by 50

3 vertially partitioned data (Poovammal and Ponnavaikko, 009). It has been shown that naïve Bayesian lassifier is extremely effetive in pratie and diffiult to improve upon. System arhiteture: The omplete implementation system arhiteture is given in Fig. 1 whih inlude data olletion modules, data analysis modules, data preproess modules, data lassifiation module and Assoiation rule mining Knowledge disovered data output module with all the internal omponent of proposed work in details. The details of all the omponent of the proposed model is given in details The proposed algorithm ANOVA T lassifiation and fuzzy D disretization is also given in details. MATERIAL AND METHODS Data analysis: Considering that an attribute X has a large number of values, the probability of the value P(X=xi C=) from Eq. an be infinitely small. Hene the probability density estimation is used assuming that X within the lass are drawn from a normal (Gaussian) distribution: 1 (x i μ ) e πσ σ σ = The standard deviation µ = The mean of the attribute values from the training set The major problem with this approah is that if the attribute data does not follow a normal distribution, as often is the ase with real-world data, the estimation ould be unreliable. Other methods suggested inlude the kernel density estimation approah. But sine this approah auses very high omputational memory and time it does not suit the simpliity of naive Bayes lassifiation). When there are no values for a lass label as well as an attribute value, then the onditional probability P(x ) will be also zero if frequeny ounts are onsidered. To irumvent this problem, a typial approah is to use the Laplae-m estimate. Aordingly: n + K P(C = ) = N+ n K n = Number of instanes satisfying C= N = Number of training instanes n = Number of lasses and k=1(predefined): J. Computer Si., 7 (4): , ni + m P(X = x i ) P(X = xi C = ) = n + m n i = Number of instanes satisfying both X=xi and C= m= (a onstant) P(X=xi) = Estimated similarly as P(C=) given above Data disretization for preproessing: Disretization is the proess of transforming data ontaining a quantitative attribute so that the attribute in question is replaed by a qualitative attribute (Pedreshi et al., 008). Data attributes are either numeri or ategorial. While ategorial attributes are disrete, numerial attributes are either disrete or ontinuous. Researh study shows that naive Bayes lassifiation works best for disretized attributes and disretization effetively approximates a ontinuous variable. The Minimum Desription Length (MDL) disretization is Entropy based heuristi given by Fayyad and Irani. The tehnique evaluates a andidate ut point between eah suessive pair of sorted values. For eah andidate ut point, the data are disretized into two intervals and the lass information entropy is alulated. The andidate ut point, whih provides the minimum entropy is hosen as the ut point. The tehnique is applied reursively to the two subintervals until the riteria of the Minimum andidate ut point, the data are disretized into two intervals and the lass information entropy is Desription Length. For a set of instanes S, a feature A and a partition boundary T, the lass information entropy of the partition indued by T is given by: S1 Ent(S1) S Ent(S ) E(A,T,S) = + s s And: Ent(S) = P(Ci, S)log (Ci, S) i= 1 For the given feature the boundary T min that minimizes the lass information entropy over the possible partitions is seleted as the binary disretization boundary. The method is then applied reursively to both partitions indued by T min until the stopping riteria known as the Minimum Desription Length (MDL) is met. The MDL priniple asertains that for aepting a partition T, the ost of enoding the partition and lasses of the instanes in the intervals indued by T should be less than the ost of enoding the instanes before the splitting. The partition is aepted only when:

4 J. Computer Si., 7 (4): , 011 Gain(A,T,S) log (N 1) Δ(A,T,S) N N > + Δ (A,T,S) = log (3 ) Ent(S) Ent(S ) Ent(S ) And: 1 1 Gain(A,T,S) = Ent(S) E(A,T,S) N = number of instanes,,1, are number of distint lasses present in S, S1 and S respetively. MDL disretized datasets show good lassifiation auray performane with naive Bayes. Classifiation on ANOVA-T data seletion: The proposed ANOVA-T statistial algorithm is used for Classifiation. Feature seletion is often an essential data preproessing step prior to applying a lassifiation algorithm suh as variane ANOVA-T. Yij = M+ ai + eij Here the M= Mean of Variables, a- standard deviation, e- Residual respetively. Standard deviation: a = (b a)(b ) d where d = ontrol group. The term feature: Seletion is taken to refer to algorithms that output a subset of the input feature set. One fator that plagues lassifiation algorithms is the quality of the data. If information is irrelevant or redundant or the data is noisy and unreliable then knowledge disovery during training is more diffiult.regardless of whether a learner attempts to selet features itself or ignores the issue, feature seletion prior to learning an be benefiial. Reduing the dimensionality of the data redues the size of the data information set and more effetively. In some ases auray on lassifiation an be improved. As a learning sheme naive Bayes is simple, very robust with noisy data and easily implementable. After the proposed statistial analysis with ANOVA-T lassifiation, attribute value represent Fig. has some irrelevant data to be removed. disretization methods, we redue the lassifiation error as shown in Fig., the estimation of p (ai < Xi bij C = ) is obtained. Beause spae limits, we present here only the version that aording to our experiments, best to redue the lassifiation error. Fuzzy-D initially forms k equal-width intervals (ai; bi) (1 i k) using EWD (equal width). Then FD estimates p (ai < Xi bi jc = ) from all training instanes rather than from instanes that have value of Xi in (ai; bi). The influene of a training instane with value v of Xi on (ai; bi) is assumed to be normal. Pseudo ode for fuzzy-d disretization: Training instane value v of x; on (a 1i,b i ) Normal distributed mean value equal to V to P(u, σ, i): bi 1 x v 1 ( ) σ P(u, σ,i) = e dx σ π ai Here, σ -> parameter Equal width disrete divides number of line V min, V max into k -> intervals, w -> width W = (Vmax V min ) = K Cut points are: Vmin + W,Vmin + W...V min + (K 1)W Here, k = 10 ie user defined parameter Equal width interval: (a i,b i)(j = 1,...,n )P(V j, σ,i) Here, n -> training instanes with known value for X; lass, Fuzzy-D Probability estimation P(ai < xi bi C = ) to be obtained by evaluation of: (ai < xi bi ^ C = ) n P(V i, σ,i) / n P j= 1 P(C = ) P(C = ) Distributed with the mean value equal to v and is proportional to: 1 x v bi Fuzzy-d disretization: Fuzzy-D disretization is 1 ( ) σ P( υ, σ,i) = e dχ ai another proposed method. By using the Fuzzy-D σ π 5

5 J. Computer Si., 7 (4): , 011 σ is a parameter to the algorithm and is used to ontrol the fuzziness of the interval bounds. Hene the Equal Width Disretization (EWD) (Yang and Webb, 00) divides the number line between V min and V max into k intervals of equal width. Thus the intervals have width: w = (Vmax Vmin) = k and the ut points are at: V min+ w,v min+ w...vmin + (k 1)w Here the k is a user predefined parameter and is set as 10 in our experiments. Suppose there are n training instanes with known value for Xi and with lass, eah with: P( υj, σ,i) Influene on: td[it] = tid list of item set it µ = fuzzy membership of any item set RESULTS In Table 1, the effiieny of ANOVA T lassifiation algorithm is ompared with existing ANOVA lassifiation algorithm. In Table, the proposed fuzzy-d disretization algorithm is analyzed by omparing with existing algorithm in alulating lassifiation error rate. In Table 3, the proposed Fuzzy- T ARM algorithm is analyzed by omparing with existing algorithm in analyzing the performane. Figure shows the performane analysis of the proposed method by omparing with the existing. The performane of the proposed method is 5 perentages higher than the existing method. Figure 3 shows the performane analysis of the proposed FTARM method by omparing with the existing FARM. The performane of the proposed method is faster than the existing method. ( i, i = a b (j 1,...,n ) Fuzzy-T assoiation rule mining: Assoiation Rule Mining algorithm preserving privay in data analysis. Our algorithm uses two phases in a partition-approah to generate fuzzy assoiation rules. The dataset is logially divided into p disjoint horizontal partitions P1, P,, Pp. Eah partition is as large as an fit in available main memory. For ease of exposition, we assume that the partitions are equal-sized, though eah partition ould be of any arbitrary size as well. We use the following notations: E = fuzzy dataset generated after pre-proessing Set of partitions P = {P1, P,, Pp} Count[it] = umulative µ of item set it over all partitions in whih it has been proessed d = number of partitions (for any partiular item set it) that have been proessed sine the partition in whih it was added. The byte-vetor-like data struture will represent the phase ode. Eah ell of the byte-vetor stores µ of the item set orresponding to the ell index of the tid to whih the µ pertains. Thus, the i th ell of the byte-vetor ontains the µ for the i th tid. If a partiular transation does not ontain the item set under onsideration, the ell orresponding to that transation is assigned a value of 0. When the byte-vetor is initialized, eah ell by default has 0. Table 1: ANOVA-T lassifiation data attributes Dataset Number of ANOVA lassifiation ANOVA T lassifiation Attribute names Data types data attributes effiieny (%) effiieny (%) Non-Relapse ontig45645_rc Continuous ontig44916_r Continuous D Continuous J Continuous Contig998_RC Continuous Contig Continuous D Continuous Contig Continuous Contig Continuous Contig3396_RC Continuous Contig1938_RC Continuous Contig Continuous AB

6 J. Computer Si., 7 (4): , 011 Table : Fuzzy-D disretization-redued lassifiation error report Dataset Number of Before disretization After fuzzy-d disretization Attribute names Data types data attributes (error rate in % ) (error rate in %) Non-Relapse ontig45645_rc Continuous ontig Continuous ontig3396_rc Continuous ontig Table.3.Performane analysis of Fuzzy-T ARM Attribute Names Fuzzy ARM attribute values Time (in se) Fuzzy -T ARM attribute values Time (in se) ontinuous Contig44916_RC ontinuous D ontinuous J ontinuous Contig998_RC ontinuous D ontinuous Contig ontinuous Contig ontinuous Contig1938_RC ontinuous AB Fig. : Performane analysis of fuzzy-d disretization Fig. 3: Performane omparison of fuzzy ARM and fuzzy T ARM 54

7 DISCUSSION In this study, we assess the performane of our algorithm with respet to fuzzy-t ARM is the most popular and widely used online fuzzy mining algorithm. We have used the breast aner dataset for our experimental analysis. The risp dataset has around.5m transations and the fuzzy dataset has around 10M transations. Thus, the dataset size is signifiantly larger than the available main memory. It an be learly observed that Fuzzy-T ARM performs 8-19 times faster than fuzzy ARM, depending on the support used. Please note that the exeution times for fuzzy ARM for support values and 0.1 have not been alulated as the time exeeded 50K seonds. From that, it is very lear that our algorithm has speeds nearly 8-13 times that of fuzzy-t ARM. More importantly, for any dataset there is a partiular support value for whih optimal number of item sets is generated and for supports less than this value, we get a flood of item sets whih are of no pratial use. From our experiments, we have observed that our algorithm performs most effiiently and speedily at this optimal support value, whih ours in the range of for this dataset. CONCLUSION In this study, we have presented a novel fuzzy- TARM algorithm, for very huge datasets, as an alternative to fuzzy ARM, whih is the most widely used algorithm for fuzzy ARM. Through our experiments, we have shown that our algorithm is faster than fuzzy ARM. This onsiderable speed up has been ahieved beause novel properties like two-phased tid list-style proessing using partitions, tid lists represented in the form of bytevetors, effetive ompression of tid lists and a tauter and quiker seond phase of proessing. REFERENCES Pedreshi, D., S. Ruggieri and F. Turini, 008. Disrimination-aware data mining. Proeedings of the 14th ACM SIGKDD International Conferene on Knowledge Disovery and Data Mining, (KDD 08), ACM New York, NY, USA., pp: DOI: / Alalá-Fdez, J., R. Alalá, M.J. Gato and F. Herrera, 009. Learning the membership funtion ontexts for mining fuzzy assoiation rules by using geneti algorithms. Fuzzy Sets Syst., 160: DOI: /j.fss Hong, T.P., Y.F. Tung, S.L. Wang, M.T. Wu and Y.L. Wu, 009. An ACS-based framework for fuzzy data mining. Expert Syst. Appl. 36: DOI: /j.eswa J. Computer Si., 7 (4): , Hu, Y.H., Y.L. Chen and K. Tang, 009. Mining sequential patterns in the BB environment J. Inform. Si., 35: DOI: / Intan, R. and O. Yenty, 008. Mining multidimensional fuzzy assoiation rules from a normalized database. Proeedings of the IEEE International Conferene on Convergene and Hybrid Information Tehnology, Aug. 8-30, IEEE Xplore, Daejeon, pp: DOI: /ICHIT Khan, N.M., C. Jahangeer, D. Goburdhun and M.H. Khan, 010. Appliation of a statistial model to biologial data analysis: Exlusive breastfeeding. Am. J. Biostat., 1: DOI: /amjbsp Mahafzah, B.A., A.F. Al-Badarneh and M.Z. Zakaria 009. A new sampling tehnique for assoiation rule mining. J. Inform. Si., 35: DOI: / Papageorgiou, E.I., 011. A new methodology for deisions in medial informatis using fuzzy ognitive maps based on fuzzy rule-extration tehniques. Applied Soft Comput., 11: DOI: /j.aso Poovammal, E. and M. Ponnavaikko, 009. Utility independent privay preserving data mining on vertially partitioned data. J. Comput. Si., 5: DOI: /jssp Qodmanan, H.R., M. Nasiri and B. Minaei-Bidgoli, 011. Multi objetive assoiation rule mining with geneti algorithm without speifying minimum support and minimum onfidene. Expert Syst. Appl.: Int. J., 38: DOI: /j.eswa Reddy, C.S. and K. Raju, 009. Improving the auray of effort estimation through fuzzy set representation of size. J. Comput. Si., 5: DOI: /jssp Vijayalakshmi, S. and V. Mohan, 010. Mining sequential aess pattern with low support from large pre-proessed web logs. J. Comput. Si., 6: DOI: /jssp Weng, C.H. and Y.L. Chen, 010. Mining fuzzy assoiation rules from unertain data. Know. Inform. Syst., 3: DOI: /s Wu, M.T., T.P. Hong and C.N. Lee An improved ant algorithm for fuzzy data mining. Proeedings of the Seond international onferene on Computational olletive intelligene: tehnologies and appliations, (ICCCI'10), Springer-Verlag Berlin, Heidelberg, pp: